Manufactured Runs

Is the 2-3 Format Fair?

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Today, the Oakland A’s and Detroit Tigers face off in an elimination game for both teams, with the winner advancing to the League Championship Series round. The A’s looked almost certain to be eliminated last night until they mustered some late-inning heroics, scraping together a three-run ninth against Tigers closer Jose Valverde.

On paper, the A’s were the higher seed coming into this series and thus were entitled to the greater home field advantage. But without last night’s miraculous win, the A’s were never going to see the benefit of their better record, due to the format of the five-game series. In order to cut down on travel days, MLB has switched to a 2-3 format—two games at home for the lower seed, then three games at home for the higher seed. In the 2-2-1 format it replaced, the team with the better record gets to take, well, advantage of their home field advantage if the series runs to three games or five games, with only a four-game series depriving them of that benefit. In the current setup, the series has to run five games for them to see the benefit of their higher seeding.

So in a different playoff series, would the A’s have needed those heroics to stay alive in the playoffs? Or would they have had an easier time dispatching the Tigers already if they hadn’t needed to force a four-game series just to see a second home game? Fans of the other higher seeds are probably wondering the same thing—of the higher seeds, the Yankees are the only team leading their series, and the Reds and Nationals are both facing elimination games today. Would those teams be in better shape right now if they’d been able to play under the old format instead of the new one?

In order to answer this question, I built a simulation that outputs the probabilities of a team winning given different sets of home and road games in a five-game series. For this purpose, I assumed that the higher seed and lower seed were evenly matched except in the matter of home field advantage. (In reality, the home seed should be a slight favorite most of the time, if home field advantage weren’t an issue.) This lets us see how the change in playoff formats affects a team’s odds of winning. Using historic data, I assumed that a home team would have a .540 winning percentage against a neutral opponent.

Let’s start by considering three-game series, which are the first possible outcome and the simplest to discuss. If either the higher seed or the lower seed sweeps those three games, the series is over. In the 2-3 format, the lower seed is actually the team with the home field advantage if the series goes to three games. So in this format, there is an 11.4 percent chance of the higher seed winning in three games, compared to 13.4 percent in the old 2-2-1 format—so, precisely a two-percent difference. Only about a quarter of these series will end in three games, and home field advantage plays a relatively small part in deciding which team sweeps. (When both teams are evenly matched, luck is the largest deciding factor—if you are uncomfortable with the word luck, what I really mean is randomness, or things unaccounted for in the simulation.) And more importantly, the chance of getting to game four is entirely unaltered by the change in playoff formats.

Going to four games is where things get more interesting. The saving grace of the format for the higher seeds is that they never face an elimination game on the road. Does that matter? It turns out that yes, in fact, it does. The benefit of being able to play game four at home means that the higher seed is more likely to win a four-game series than it would be under the old format, where two elimination games occur on the road. This format actually raises the odds of the higher seed winning the series in four games, from 17.8 percent to 19.7 percent, almost exactly what we saw above. (Actually, while the rounded figures show a slight difference, the raw figures show the same gains in the chance of winning in four games as they show a lowering of the odds of winning in three games.) And then in five games, the odds of winning the series are exactly the same as they were before.

So the new format isn’t to blame for the showing of the higher seeds in this year’s playoffs. All of them managed to avoid being swept, thus forcing terms at least as favorable to them as what they would have seen under the old playoff format. Major League Baseball is still planning to switch back to the old format for next year, but the owner’s interest in this probably has more to do with finances than fairness. (While playoff teams split ticket revenue equally, there are likely ancillary financial benefits to hosting a home playoff game that make it desirable to host them yourself rather than simply getting your cut of the gate from a road playoff game.) The simple truth is that teams haven’t been cheated out of wins by the 2-3 format.

And to the home team go the concessions... not inconsiderable when you're selling 40 000 tickets. There's not a lot of difference between the teams at this point in the season, making home field advantage even less of a factor.

Interesting. The perception that the new format is less advantageous for the higher seeds probably stems from the belief that it is more difficult to win consecutive games, i.e. that allowing the lower seeded team to win 2 games at home forces the higher seed to win 3 in a row, which is more difficult than winning any 3 independent games. That shouldn't be true in an infinitely long season, but maybe it has some merit when we're talking about consecutive "win or go home" games. Maybe being faced with elimination changes team performance in a way that lowers the odds of winning games, or at least consecutive games. For example, a team pulls its starter early and blows through its bullpen in an elimination game, decreasing its win expectancy in subsequent games, when it would otherwise have ridden the starter longer to no detriment (let's say the team ends up scoring 5 runs a couple innings later and had a greater cushion than it realized). I can throw out other theoreticals, but they all stem from the possibility that win probabilities in playoff series are conditional and not independent as you assumed in your simulation. Do you think there's any merit to that?

I've seen research from other sports suggesting that the score in the series significantly impacts a team's winning percentage - especially when teams are facing elimination games. While I haven't seen anything on whether this works in baseball, it would be interesting to see how that might work through if it did apply to baseball.

"The simple truth is that teams haven’t been cheated out of wins by the 2-3 format."

Teams in general, but not necessarily specific teams. Both Oakland and Detroit performed substantially better than .540 at home this season (.607), and while Oakland was quite a bit better than average on the road (.543), Detroit was not (.469). As an A's fan, I also worried about facing Verlander at Comerica in Game 1 - over the past four seasons, his ERA has been more than a run-and-a-half better at home. Now they get to face him at home, of course, but it would've been much better if they could've avoided this game entirely.

No. It is an advantage to be at home with your ace on the mound. Most teams have a higher winning percentage in that situation. What this article is saying is that this doesn't matter much in the long run of the series in terms of results (although we have a very small sample size for 2-3 series), but in practical terms it means that the "advantaged" team, if playing against a "disadvantaged" team that plays much better at home than on the road, is no longer "advantaged" by this format -- it basically says "home field advantage only matters in the out games, and if we have a case that the team with the lower record has a bigger home advantage by record, then we don't care, because you should overcome it". It's like affirmative action for home field, and it's stupid.

I think it's unfair as I've always said the team with home field advantage, should home field hold up throughout the series, should never have to face an elimination game until the final game of the series. With 2-3 format the team with advantage could potentially face 3 straight elimination games, completely wrong IMHO. The elimination game pressure should fall on the "weaker" team.

For me, the 2-3-2 format was always about *evening out* the advantage across the teams. In other words to nullify, as much as possible, the home field advantage. Perfect for the World Series, I think, at least before this interleague regular season abomination. Not for leagues where you wish to reward the team with the best record (NBA, NHL).

Thanks for writing this. Honestly, I thought this had been pointed out years ago, and I've been absolutely baffled by the overwhelmingly negative response to the new format. This is how it should always have been, and how it should remain.

I agree with this. It gives homefield advantage a little more oomph if you get three home games to start off, and it makes things that much more exciting for the underdogs if they get to game 5. Good from a financlial point of view too. Why not incentivize getting a high seed?

I would prefer 2-2-1. That way you can't just sweep in by means of home field, but you also can't be coming back home to your first "home field advantage" game as an elimination game. Sorry, but that is just turning the whole concept of advantage on its head.